I have a matrix Z n times p with p>n
I have A a diagonal matrix with positive entries
I would like to know if there is a knwon relation (as a function of A) between
the MP inverse of Z^T Z
and the MP inverse of A Z^T Z A
what i am looking for is the follwing: suppose I knwo the MP of $Z^T Z$ and I know $A$, can I get as a function of those two things the MP inverse of $A Z^T Z A$?